Timeline for Grönwall-type inequality for $f(t) \le \alpha + \int_0^t (t-s)^{-\frac{1}{2}} [f(s) + |f(s)|^{\beta}] \, \mathrm d s$
Current License: CC BY-SA 4.0
6 events
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| Mar 26 at 21:09 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Mar 26 at 20:58 | vote | accept | Akira | ||
| Mar 26 at 20:58 | comment | added | Iosif Pinelis | @Akira : I think this can be done, say by an iteration argument and using Jensen's inequality. However, as your present question has been answered, I suggest you post the additional question separately. | |
| Mar 26 at 20:50 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Mar 26 at 20:47 | comment | added | Akira | Thank you for your answer! I wonder if we can obtain a tight upper bound in the sense that if $\alpha=0$ then $f=0$. | |
| Mar 26 at 20:38 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |